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Sibirskii Matematicheskii Zhurnal, 2001, Volume 42, Number 3, Pages 567–584 (Mi smj1445)  
This article is cited in 7 scientific papers (total in 7 papers)

Justification of the steepest descent method for the integral statement of an inverse problem for a hyperbolic equation

S. I. Kabanikhina, K. T. Iskakovb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b E. A. Buketov Karaganda State University
Full-text PDF (243 kB) Citations (7)
Abstract: Under consideration is the steepest descent method for solving the problem of determination of a coefficient in a hyperbolic equation in integral statement. The properties of solutions to the direct and inverse problems are studied. Estimates for the objective functional and its gradient are obtained. Convergence in the mean is proved for the steepest descent method for minimizing the residual functional.
Received: 15.02.1999
English version:
Siberian Mathematical Journal, 2001, Volume 42, Issue 3, Pages 478–494
DOI: https://doi.org/10.1023/A:1010471125870
Bibliographic databases:
UDC: 517.95
Language: Russian
Citation: S. I. Kabanikhin, K. T. Iskakov, “Justification of the steepest descent method for the integral statement of an inverse problem for a hyperbolic equation”, Sibirsk. Mat. Zh., 42:3 (2001), 567–584; Siberian Math. J., 42:3 (2001), 478–494
Citation in format AMSBIB
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\by S.~I.~Kabanikhin, K.~T.~Iskakov
\paper Justification of the steepest descent method for the integral statement of an inverse problem for a~hyperbolic equation
\jour Sibirsk. Mat. Zh.
\yr 2001
\vol 42
\issue 3
\pages 567--584
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\zmath{https://zbmath.org/?q=an:0981.35097}
\transl
\jour Siberian Math. J.
\yr 2001
\vol 42
\issue 3
\pages 478--494
\crossref{https://doi.org/10.1023/A:1010471125870}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000169277100008}
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  • https://www.mathnet.ru/eng/smj/v42/i3/p567
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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